This appendix is written as a stand-alone report of the sum-rule relationships needed to insure that all inelastic scattering amplitudes (all \(2\rightarrow 2\)  scattering amplitudes with massive spin-2 fields of arbitrary mode number in the external states) grow no faster than \({\cal O}(s)\)  and report which we have succeeded in proving – completing the program begin in [1]}, [2]}, [3]}, [4]}. Section REF  derives relationships used in Sec. REF  of the main body of this paper and can be read independently.
